In this paper, we describe a rate equation approach that leads to new insights about electrical breakdown in insulating and semiconducting materials. In this approach, the competition between carrier generation by impact ionization and carrier recombination by Auger and defect recombination leads to steady state solutions for the carrier generation rate, and it is the accessibility of these steady state solutions, for a given electric field, that governs whether breakdown does or does not occur. This approach leads to theoretical definitions for not only the intrinsic breakdown field but also other characteristic quantities. Results obtained for GaAs using a carrier distribution function calculated by both a Maxwellian approximation and an ensemble Monte Carlo method will be discussed.